Electrical conductivity is a physical parameter in the mantle that can be estimated from the surface, as well as seismic wave velocities. Many researchers have been therefore measuring the electrical conductivity of crust and mantle rocks.
One of problems with electrical conductivity in the mantle is that conductivity at the top of the asthenosphere (around 100 km depth) near the mid-oceanic ridge is higher than expected from dry olivine, which is referred to as the high-conductivity layer (HCL). Although some researchers attempted to explain the HCL based on the proton conduction (i.e. migration of free proton) of olivine, the magnitude of proton conduction by H2O contents of depleted MORB mantle is too low to explain the HCL. Another possible explanation is that the HCL could be caused by trace amounts of partial melt. Partial melts are, however, difficult to stay in particular depth because of high permeability of melts in rocks and lower density of melt than rocks under asthenospheric conditions.
On the other hand, we recently discovered a new mechanism to interpret the high conductivity anomaly: the ionic conductivity by Mg vacancy is greatly enhanced by trace amounts of H2O incorporation. Although it is still unclear whether this mechanism can explain the high conductivity, and therefore we need further investigation.
H2O enhancement of ionic conductivity of olivine [Fei et al., 2018; 2020]
Electric conductivity of the oceanic asthenosphere [Katsura et al., 2017]